Electron-Positronium Scattering and the Photodetachment of the Positronium Negative Ion*

Following the experimental observation of the positronium negative ion (Ps^-), we studied theoretically electron-Ps scattering and the photodetachment of this ion below the Ps(n=2) threshold [1-3]. We employed both the Kohn and inverse Kohn variational methods with highly correlated trial functions to compute ^1,3S and ^1,3P wave phase shifts for electron-Ps scattering. We also determined the binding energy of Ps^- using the Rayleigh-Ritz variational method and a Hylleraas trial function [2]. Using the  bound-state wave function and the ¹P electron-Ps continuum wave function determined from the Kohn variational method, we computed the photodetachment cross section in both the length and velocity forms. For the higher energies that we considered, our results of the photodetachment cross section differ from both the hyperspherical close-coupling results [4] and the B-spline close coupling results [5]. Due to this discrepancy and the  observation of the photodetachment of Ps^- [6], William Mitchell and I have computed the photodetachment cross section in the length and velocity forms.  We used a larger basis set for the bound-state wave function than previously employed [1-3]. Also, we used the Kohn, inverse Kohn and complex Kohn variational methods for the ¹P continuum wave function.  These recent cross section results are consistent with the prior variational results [1-3]. Very recently, we have computed the photodetachment cross section in the acceleration form using variationally determined wave functions. In addition to computing the ¹P phase shifts for electron-Ps scattering, we have computed the ^1,3S and ³P phase shifts and have begun a calculation to compute the ^1,3D phase shifts.

 

[1] S. J. Ward and M. R. C. McDowell, Europhys. Lett. 1, 167 (1986).

[2] S. J. Ward, Thesis, University of London, Unpublished (1986).

[3] S. J. Ward, J. W. Humberston and M. R. C. McDowell, J. Phys. B 30, 127 (1987).

[4] A. Igarashi, I. Shimamura and N. Toshima, New J. Phys. 2, 17 (2000).

[5] A. Igarashi, S. Nakazaki, and A. Ohsaki, Phys. Rev. A 61, 032710 (2000).

[6] Y. Nagashima, PlenaryIPlenary Talk at the 18^th International Conference on Positron Annihilation (ICPA-18), 2018.